By K. Nachazel

Methodological tactics of the speculation of estimation of statistical parameters of time sequence and their program to hydrology and water engineering, fairly the field of reservoir-controlled runoffs, are handled during this quantity. For estimates use is made up of random sequences generated for varied chance homes. This methodological strategy permits exam of the homes of random and systematic blunders of the parameters predicted even for the asymmetrical chance distributions, that are common in hydrology and water engineering. This booklet could be of curiosity to stochastic hydrologists.

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The research carried out has however also revealed some problems of statistical analysis, which will require some attention. Basically, these problems follow from the complex probability (particularly autocorrelative) properties of some of the time series. As far as the methods of filtration are concerned, the greatest problems were posed by the estimation of the weight coefficientsand the degree of filtration. And besides, it is obvious that with the length of the series avilable being limited, no high degree of filtration can be chosen, because the series filtered gets shorter and its analysis is thus made more difficult.

Joint density is thus resolved into several functions that depend both upon value x of the random variable and upon the value of the unknown parameter 8. 33 Sample characteristics. Their distribution If X = (X,, ... 32) V(X) where n S j ( X ) = Sj(X1, ... , k, i= 1 n V(x) = c V(Xi). 33), represent the highest possible reduction of the results of observation, and the most expedient replacement of all the n observations by a lower number of data. They are therefore referred to as minimum sufficient statistics.

A For the construction of the best unbiassed estimators a special class of distribution - the so-called exponential class of distribution - is of importance. Variable X has a distribution of an exponential type, if its probability density function f ( x ) can be written in the following form [35, 65,921: " f ( x ;8) = ~ X P C j= 1 + R ( 8 ) + v( Qj(@)uj(x) and if it satisfies the following conditions: set { x 1 f ( x ; @) > 0) is independent of 8, parameter space Q contains a k-dimensional interval, i.

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